1. Field of the Description
The present invention relates, in general, to combining printed images with lens arrays to display three dimensional (3D) images with or without motion, and, more particularly, to a method of pixel mapping, providing arrangements of pixels, and imaging that is adapted for use with arrays of square or round-based micro lenses to provide enhanced 3D imagery with fuller volume and/or with multi-directional motion.
2. Relevant Background
There are presently many applications where it is desirable to view a printed image via an array of lenses. For example, anti-counterfeiting efforts often involve use of an anti-counterfeiting device or element that is made up of an array of lenses and an image printed onto the back of the lens array or onto an underlying substrate or surface (e.g., a sheet of paper or plastic). The anti-counterfeiting element may be used to display an image that is chosen to be unique and be an indicator that the item carrying the anti-counterfeiting element is not a counterfeit. The anti-counterfeiting market is rapidly growing worldwide with anti-counterfeiting elements placed on a wide range of items such as upon currency (e.g., on a surface of a paper bill to help prevent copying) and on labels for retail products (e.g., labels on clothing showing authenticity).
In this regard, moiré patterns have been used for years in anti-counterfeiting elements with arrays of round lenses and with arrays of hexagonal arrays (or round and hexagonal lens arrays). Typically, the printed images provided in an ink layer under these lens arrays are small, fine images relative to the size of the lenses. A moiré pattern is provided in the printed images in the form of a secondary and visually evident superimposed pattern that is created when two identical patterns on a surface are overlaid while being displaced or rotated a small amount from each other.
In such moiré pattern-based anti-counterfeiting elements, some of the images may be printed in a frequency slightly more or less frequent than the one-to-one dimension of the lenses in two axes, and some of the images may be printed slightly differently relative to each other. FIG. 1 illustrates an exemplary assembly 100 that may be used as an anti-counterfeiting element. The assembly 100 includes a lens array 110 made up of side-by-side, parallel columns (or rows) 112 of round lenses 114, and it can be seen that the columns 112 are offset from each other (by about 50 percent) such that pairs of adjacent lenses 114 in the columns are not aligned (e.g., a lens in a next column is positioned in the space between two lenses in the previous column).
A printed image 120 is provided in a layer of ink underneath the lens array 110 (on a back, planar surface of the lens array 110). The result, which is difficult to see in FIG. 1, is a moiré pattern that provides the illusion of depth of field to a viewer via the lenses 112 of the array 110 or, in some cases, the sense that the images are moving (motion or animation of the displayed items). Typically, the thickness of each of the lenses 112 is in the range of 0.5/1000 to 5/1000 inches (or 12 to about 125 microns), and the frequency of these lenses 112 in an array 110 is about 400×400 to over 1000×1000 per inch.
While helpful to reduce counterfeiting, use of moiré patterns with round lens arrays has not been wholly satisfactory for the anti-counterfeiting market. One reason is that the effects that can be achieved with moiré patterns are limited. For example, one cannot take a photograph and display 3D with a moiré pattern. Generally, the moiré patterns are used in the security and/or anti-counterfeiting industry in very fine lenses with focal lengths of about 20 to 75 microns and frequencies of over 500 lenses per inch in one axis or more than 250,000 lenses per square inch. As a result, the images underlying the lenses in the lens array are typically printed at least at 12,000 DPI (dots per inch) and may even be provided at over 25,000 DPI. These micro-lens arrays are generally closely nested as shown in element 200 with its array 210 in FIG. 2. The array 210 uses hexagonal lenses that are provided in offset and overlapping columns 212 (e.g., side-by-side lenses 214 are not aligned in a row and are positioned to fill or be nested into space between two lenses of adjacent columns 212) to focus on an image or moiré pattern 220 in an underlying ink layer.
One problem or issue with the use of such an array 210 and images 220 is that the element 200 is relatively easy to reverse engineer, which limits its usefulness as an anti-counterfeiting element. Particularly, the patterns 220 underlying the lenses 214 can be seen with an inexpensive and readily available microscope, which allows one to determine the frequency of the images and patterns. In addition, the lenses 214 can be cast and re-molded, which leaves printing the identified images as the only hurdle for successfully copying the element 200 (and then counterfeiting a piece of currency or a label for a product). Unfortunately, printing the image 220 is becoming easier to accomplish due to high resolution lasers and setters and other printing advances. Typically, for an element 200, the micro-lenses are printed using an emboss and fill technology, which limits the printing to one color due to the fact that the process tends to be self-contaminating after one color and also due to the fact that the process is difficult to control from a relative color-to-color pitch in the emboss-and-fill printing process.
Hence, there remains a need for advancements in the design and fabrication of assemblies or elements that combine a lens array with a printed image (layer of ink containing images/patterns) to display imagery. Such improvements may allow new anti-counterfeiting devices or elements to be produced for use with currency, labels, credit/debit cards, and other items, and these anti-counterfeiting devices preferably would be much more difficult if not nearly impossible to duplicate or copy. Further, there is a growing demand for such anti-counterfeiting devices to provide a surprising or “wow factor” with their displayed imagery such as images that float above and/or below a focal plane (e.g., more true 3D displays).